On the Architecture and Reasoning of Large Language Models

This thesis investigates two complementary axes for improving Large Language Models (LLMs): the architecture used during pretraining, and the reasoning behavior elicited during post-training. The first part of the thesis addresses well-documented optimization pathologies of deep Transformer language models that limit the effective utilization of depth. We first present Gradient-Preserving Activation Scaling (GPAS), a residual-stream plugin that combats the exponential growth of activation variance — the root cause of residual-shortcut dominance over sub-layer outputs and the degraded learning of deeper layers, most acute in the Pre-LayerNorm (Pre-LN) Transformer — by scaling down intermediate activations while preserving their gradients. GPAS avoids the gradient-vanishing pathology of naive downscaling and yields consistent gains at model sizes from 71M to 1B parameters across Pre-LN, Post-LN, DeepNorm, Sandwich-LN, Mix-LN, and LayerNorm-Scaling. Building on this line of work, we then introduce Progressive Residual Warmup (ProRes), a depth-aware optimization curriculum that gradually warms up each layer’s residual contribution from zero to one, with deeper layers waiting longer than shallow ones; this “early layers learn first” inductive bias stabilizes optimization across initialization and normalization schemes and produces a distinctive trajectory that yields faster convergence, stronger generalization, and better downstream performance. The second part of the thesis turns to reasoning. We present Double-Checker, a self-critical fine-tuning framework that teaches slow-thinking, long chain-of-thought LLMs to explicitly critique their own intermediate solutions and iteratively refine them until the model judges its answer correct under its own critique. With only 1,730 carefully curated self-critical instances, Double-Checker substantially improves the reasoning accuracy and self-correction reliability of strong slow-thinking baselines. Together, these contributions improve modern LLMs along two complementary axes: macro-architectural interventions that improve training stability and depth utilization during pretraining, and lightweight self-critical fine-tuning that elicits more reliable reflective reasoning after pretraining.